On positive solutions of one problem with heterotone operator and the construction of successive approximations

Abstract

In this paper, the existence, uniqueness and possibility of constructing of two-sided approximations to the positive solution of the nonlinear elliptic boundary problem are considered. An investigation of the problem is based on methods of operator equations theory in half-ordered spaces. Conditions that link the parameters in order to ensure the existence and uniqueness of the positive solution are obtained as well as conditions needed for construction of two-sided approximations. The results of the computational experiment are presented as a table, plots of approximate solution surface, level lines and a cross section. They are compared with the results obtained by Green's quasifunction method.